A380559 With p(n) = A002144(n) = n-th Pythagorean prime, a(n) is the least k such p(n) + k is a Pythagorean prime and 2 p(n) + k - 1 is a Pythagorean prime; set a(n) = 0 if there is no such k.
8, 4, 20, 32, 16, 20, 8, 28, 28, 20, 4, 56, 40, 44, 20, 92, 24, 8, 12, 4, 116, 4, 44, 28, 56, 80, 4, 32, 56, 36, 20, 36, 4, 56, 16, 20, 4, 8, 12, 12, 16, 152, 64, 140, 32, 20, 16, 104, 44, 40, 8, 12, 4, 44, 20, 56, 40, 28, 56, 8, 64, 24, 40, 92, 60, 56, 140
Offset: 1
Keywords
Examples
5 + 8 = 13, the least Pythagorean prime after 5, and 5 + 13 - 1 = 17, a Pythagorean prime, so a(1) = 8.
Programs
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Mathematica
s = Select[Prime[Range[450]], Mod[#, 4] == 1 &] a[n_] := Select[Range[200], MemberQ[s, s[[n]] + #] && PrimeQ[2 s[[n]] + # - 1] &, 1] Flatten[Table[a[n], {n, 1, 140}]]